Twisted index theory on good orbifolds, I: noncommutative Bloch theory
Differential Geometry
2007-05-23 v1 Mathematical Physics
K-Theory and Homology
math.MP
Operator Algebras
Abstract
This paper, together with Part II, expands the results of math.DG/9803051. In Part I we study the twisted index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective action of the orbifold fundamental group. We apply these results to obtain qualitative results on real and complex hyperbolic spaces in 2 and 4 dimensions, related to generalizations of the Bethe-Sommerfeld conjecture and the Ten Martini Problem, on the spectrum of self adjoint elliptic operators which are invariant under a projective action of a discrete cocompact group.
Keywords
Cite
@article{arxiv.math/9911102,
title = {Twisted index theory on good orbifolds, I: noncommutative Bloch theory},
author = {Matilde Marcolli and Varghese Mathai},
journal= {arXiv preprint arXiv:math/9911102},
year = {2007}
}
Comments
34 pages, LaTex